New Trends in Free Boundary Problems

Abstract

We present a series of recent results on some new classes of free boundary problems.Differently from the classical literature, the problems considered have either a “nonlocal” feature (e.g., the interaction or/and the interfacial energy may depend on global quantities) or a “nonlinear” flavor (namely, the total energy is the nonlinear superposition of energy components, thus losing the standard additivity and scale invariances of the problem).

Keywords

• free boundary problems
• nonlocal equations
• regularity theory
• free boundary conditions
• scaling properties
• instability
• 35r35
• 35r11